Signal flow graphs vs fuzzy cognitive maps in application to qualitative circuit analysis
International Journal of Man-Machine Studies
Combinatorial algorithms: generation, enumeration, and search
ACM SIGACT News
Journal of the ACM (JACM)
The Combinatorics of Network Reliability
The Combinatorics of Network Reliability
On the existence and construction of T-transitive closures
Information Sciences: an International Journal
Brain tumor characterization using the soft computing technique of fuzzy cognitive maps
Applied Soft Computing
Fuzzy cognitive map modelling educational software adoption
Computers & Education
A fuzzy cognitive map approach for effect-based operations: An illustrative case
Information Sciences: an International Journal
Application of fuzzy cognitive maps for cotton yield management in precision farming
Expert Systems with Applications: An International Journal
Using fuzzy cognitive map for the relationship management in airline service
Expert Systems with Applications: An International Journal
Modeling complex systems using fuzzy cognitive maps
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
On causal inference in fuzzy cognitive maps
IEEE Transactions on Fuzzy Systems
Algorithms for the computation of T-transitive closures
IEEE Transactions on Fuzzy Systems
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We define a bipolar weighted digraph as a weighted digraph together with the sign function on the arcs such that the weight of each arc lies between 0 and 1, and no two parallel arcs have the same sign. Bipolar weighted digraphs are utilized to model so-called fuzzy cognitive maps, which are used in science, engineering, and the social sciences to represent the causal structure of a body of knowledge. It has been noted in the literature that a transitive closure of a bipolar weighted digraph contains useful new information for the fuzzy cognitive map it models. In this paper we ask two questions: what is a sensible and useful definition of transitive closure of a bipolar weighted digraph, and how do we compute it? We give two answers to each of these questions, that is, we present two distinct models. First, we give a review of the fuzzy digraph model, which has been, in a different form and less rigorously, studied previously in the fuzzy systems literature. Second, we carefully develop a probabilistic model, which is related to the notion of network reliability. This paper is intended for a mathematical audience.